CINCINNATI — The video advertising board outside Paul Brown Stadium flashed a sign on Monday afternoon that proclaimed, “We Win!”

And that, pretty much, was the extent of the celebration.

No longer winless, the 1-8 Cincinnati Bengals headed into their bye week happy about a few small accomplishments. They will still go down in franchise history as one of the worst-starting teams, but not the very worst. And they can let the 0-8 Detroit Lions field all the “Think you can go 0-16?” questions from here on out.

Not much, but it’s something.

A 21-19 victory over Jacksonville on Sunday gave the Bengals not only their first win of the season, but their first celebration at Paul Brown Stadium all year. They dropped both of their home preseason games, including a 13-0 loss to New Orleans in which Carson Palmer got his nose broken and the Bengals never advanced beyond the Saints’ 47-yard line.

“Relief is one of the biggest words,” quarterback Ryan Fitzpatrick said.

That good feeling may not have much shelf life. When the Bengals return, they face a daunting schedule and some of the same old problems that got them to this point.

Coach Marvin Lewis said Monday there was nothing new to report on Palmer, who has missed the last four games with an injured passing elbow. Palmer has declined to talk about the injury, sustained when his arm was hit while he threw a pass against the Giants on Sept. 21.

Palmer is getting physical therapy, hoping the elbow will heal without surgery. He wants to play again this season, even though there’s no real reason to do so other than to show leadership.

At some point this month, Palmer will have his elbow re-evaluated to see if it’s healing properly or if his season is over.

“But for now, it’s going to wait,” Lewis said.

The victory over the self-destructive Jaguars provided hope that the offense can finally get going without Palmer. The Bengals were last in the league on offense heading into the game.

Fitzpatrick got his first NFL victory as a starter, throwing a couple of touchdown passes to Chad Ocho Cinco. The coaches seem to have gotten a better feel for what he does best: Scramble away from pressure, throw short passes on the run.

“I think it’s them knowing me better and me knowing them better, in terms of my style of play,” said Fitzpatrick, who went 19-of-26 while the Bengals pulled ahead 21-3. “I felt really comfortable in the first half, and I think it showed in the two touchdown drives that we had.”

The Bengals got their first 100-yard rusher of the season. Cedric Benson ran for 104 overall, and had the team’s longest run of the season at 30 yards.

The Bengals also showed a little more fight than they had all season. Offensive tackle Andrew Whitworth took a few left-handed swings at Jacksonville defensive tackle John Henderson after he knocked off Whitworth’s helmet, then appeared to try to gouge his eyes. Both players were penalized and ejected.

“I just pushed him past the quarterback, and he fell to the ground,” Whitworth said. “But he held onto my facemask and ripped my helmet off. I turned to go back to the play, and the next thing I knew, I felt him grabbing at my eyeballs. I really didn’t know what to do when someone’s fingers are trying to dig into my eyes.”

Lewis didn’t fault Whitworth, who cost the Bengals field position by taking a swing at Henderson.

“Whit was not retaliating,” Lewis said. “Whit was trying to defend himself. It’s a shame. He feels bad about it because it took us out of position, and we lost a very good player. That’s the shame of it.”

Whitworth’s don’t-back-down attitude was appreciated by his teammates, who got the feeling that the rest of the league was starting to look at them as doormats.

“I don’t know if teams felt they could come over here and walk over us,” receiver T.J. Houshmandzadeh said. “I felt that teams, when they came to play us, everybody thought they were going to win — coaches, players, equipment men, trainers. I really thought that they thought they would win, everybody we played.

“We’re good at 1-8. It’s a terrible thing to say. We’ve got a good team. We’re just not winning enough games.”